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Simplifying ln(7x) + ln(5x) = ln(36) Remove parenthesis around (7x) ln * 7x + ln(5x) = ln(36) Reorder the terms for easier multiplication: 7ln * x + ln(5x) = ln(36) Multiply ln * x 7lnx + ln(5x) = ln(36) Remove parenthesis around (5x) 7lnx + ln * 5x = ln(36) Reorder the terms for easier multiplication: 7lnx + 5ln * x = ln(36) Multiply ln * x 7lnx + 5lnx = ln(36) Combine like terms: 7lnx + 5lnx = 12lnx 12lnx = ln(36) Reorder the terms for easier multiplication: 12lnx = 36ln Solving 12lnx = 36ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-36ln' to each side of the equation. -36ln + 12lnx = 36ln + -36ln Combine like terms: 36ln + -36ln = 0 -36ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '12ln'. 12ln(-3 + x) = 0 Ignore the factor 12.Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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